Sources of Gravitational Waves: an Overview Bernard Schutz Albert Einstein Institute Potsdam, Germany @aei.mpg.de

Sources of Gravitational Waves: an Overview

Bernard Schutz

Albert Einstein Institute

Potsdam, Germany

http://www.aei.mpg.de [email protected]

Bernard F Schutz Albert Einstein Institute

24 April 2003

Astrogravs: Overview of GW Sources

2

Gravitational Wave Physics• GW observations will require a mix of five key ingredients:

1. good detector technology2. good waveform predictions3. good data analysis methodology and technology4. coincident observations in several independent detectors5. coincident observations in electromagnetic astronomy

• Source studies aim at 2. and 5., and at understanding what information is likely to come from observations. They underpin 3. Source studies require input from GR and from astrophysics.

• Waveform predictions: the nonlinearity of GR makes detailed computation of sources difficult. But nonlinearity is an essential part of the problem, since almost all sources are driven to radiate by self-gravitation. (Exception: GW pulsars.)

• Astrophysics input helps focus effort on the most interesting and/or promising sources: theory/modeling & data-analysis effort.


24 April 2003


3

Tools of the trade• The two-body problem has been studied with 2 methods:

– post-Newtonian methods (weak-field/low-velocity) – radiation-reaction methods (restricted 2-body problem, one mass

very small).

• The one-body problem (isolated NS/BH oscillations) can be studied with perturbation approximations.

• “Cosmic modesty” of BHs seems to allow study even of dynamical BH pairs by the close-limit approximation.

• Outside these regimes, and for most other sources, numerical simulation studies are our only hope.

• To guide astrophysical estimates, where waveform predictions are not required, quasi-Newtonian order-of-magnitude formulas are useful.


24 April 2003


4

Gravitational Waves in a Quasi-Newtonian Nutshell

• Generation: r/dtId

c2G

h2TT2

4

h

2rc

GM

2Rc

GM

Newtonian potential

internal potential

F32π1

Gc3 2

h

all classical field theories

dimensional factor

• Upper limit:

• Energy Flux:

4G

f2


24 April 2003


5

Polarization• Gravitational waves have 2 independent polarizations, illustrated

here by the motions of free “test” particles.

• They follow the motions of the source TT-projected on the sky.• Interferometers are linearly polarized detectors.• A measurement of the degree of circular polarization determines

the inclination of a simple binary orbit. If the orbit is more complex, as for strong spin-spin coupling, then the changes in polarization tell what is happening to the orbit.


24 April 2003


6

Gravitational Dynamics

• Luminosity

• Frequency f 2 1

4G

L 4 2r F1

32cG

3

h 2

( )2 2fh

FHG

IKJ

332

5

2

5cG

GMRc

very strong dependenceon compactness

M 43

3RFHG

IKJ/

• Timescale / LGMR

2

2

FHG

IKJ

163 2

3Rc

GMRc

Chirp time is a measure of light-crossing time


24 April 2003


7

Detectors Measure Distances:Chirping Binaries are Standard Candles

If a detector measures not only f and h but also for a binary, then it can determine its distance r.

For a circular binary, upper bounds are attained, so:

f 33

1 2GMR

FHG

IKJ

/163 2

3Rc

GMRcFHG

IKJ

FHG

IKJ

16

3 2

5 2GMRc

/

.

Combining this with f itself gives us M and R, and then the value of h gives us r, the distance (luminosity distance ).

If a chirping massive black-hole binary is identified so that a redshift can be obtained, then one can do cosmology: H0, q0. LISA can measure f, , and h to 0.1% accuracy.


24 April 2003


8

GW physics across the spectrum

810low

high

f

f

A chirping system is a GW standard candle: if positionis known, distance can be

inferred.

2 x 100 M BHs coalesce in 1 yr

from ~ 0.1 Hz


24 April 2003


9

Kicks and Binary Lifetimes• Pure quadrupole radiation carries no net linear momentum.

To get a kick you need quadrupole-octupole coupling, whose flux is down by a factor of v/c from quadrupole.

• The momentum flux P is the energy flux c, so the total radiated momentum (allowing for angular factors) is at most 0.2 Lv/c2. Assuming that this happens in the last half orbit (Pmin/2) leads to a recoil velocity no larger than

• Holes must come within a separation Rmax to coalesce in a Hubble time, where

1-342

minrecoil s km 300102.11.0 c

c

GL

Mc

LvPv

pc. 10

1054/3

Sun6

4max

M

MR


24 April 2003


10

Taxonomy of GW Waveforms

Chirping or coalescingNS, BH binaries

LIG O I, Adv LIGO

G rav. CollapseAdv LIG O , LISA

NS vibrationf-, p-, r-, w -m odes

Adv LIGO , HF detectors

Unm odelled,unexpected

All detectors

BurstsShort, no phase

m odulation

G W PulsarsLIG O I, Adv LIGO

G alactic binariesLISA

SM BH coalescenceLISA

G ravitational capturesLISA

LM XBsAccretion-driven

G W em issionAdv LIGO

CWContinuous in

source rest-frame

Cosm ic GW BkgndAll detectors

Astrophysical BkgndsLISA

StochasticRandom ; broad

spectrum

G W Sources

1

2

3

4

5

6


24 April 2003


11

Chirping and coalescing binaries

• LIGO I/GEO/VIRGO could see BH CBs to 100 Mpc, may be first detected source

• Adv LIGO should see many BH CBs per year to z~0.5• Range very dependent on masses and on modeling of late-

stage waveform• Adv LIGO should see similar numbers of NS coalescences

out to ~500 Mpc. • No NS-BH binaries in Galactic pulsar population yet• LISA will see SMBH coalescences 104-107 M everywhere,

also 100 + 104 M coalescences to z~1.• LISA will see chirping WD, NS binaries in Galaxy, predict

future coalescences, measure distances


24 April 2003


12

Black-Hole Coalescences

• Early inspiral well-understood using pN methods, getting even better.

• Transition, plunge, merger still needs work.

• Possible first source for LIGO I/GEO/VIRGO, confidence difficult!

• Most spectacular source for LISA, huge S/N

• Event rates for LIGO, LISA very uncertain

Population:

Waveform:

Potential for the unexpected:

Data analysis:


24 April 2003


13

Issue: BH Merger Simulations

• Improving all the time:– More stable forms of the field equations– Gauge conditions improved– Run times lengthening– Initial data must be improved: subtle– Boundary conditions not yet satisfactory

• EU- funded network “Sources of Gravitational Waves” pushing all of these issues.

• Still hungry for computer time. The Discovery Channel funded AEI’s longest simulation to date, and its visualization. (Seidel, Benger, et al, AEI)


24 April 2003


14

Black-Hole Simulations: Next Steps• Still very far from having reliable waveforms• Adaptive, dynamical mesh refinement needed to give good

resolution with long run times• Stability of codes still an issue past 50 M• Run time an issue: Lazarus • Outer boundary condition a critical issue• Initial data exploration essential, unequal masses too• Is the plunge sudden or gradual?• EU network has applied for (an will probably get)

renewal/extension. Will soon be a NASA-NSF initiative to stimulate work here. In my view the field needs several complementary collaborations.


24 April 2003


15

Black Hole Binary Populations• Manufactured in globular clusters, more work

needed on GC evolution, early GC population, …• SMBH binaries: many uncertainties --

– Growth of SMBHs (by merging of smaller holes or by accretion?)

– Timescale for galaxy mergers to produce BH mergers– Relation of binary pairs and recent mergers to galactic

activity

• Very active area of research (this conference!)


24 April 2003


16

Data analysis for CBs

• Construction of search templates for NS-NS binaries well understood, most S/N from inspiral

• More massive systems shift to lower frequency, so for LIGO the S/N becomes more dependent on the plunge-merger phase. Don’t yet know how best to do these searches.

• LISA: SMBH coalescence will be visible without filtering, but good fitting needed to remove signals without contaminating weaker signals also present. Not clear if this will be possible for merger phase (a few minutes for each event).


24 April 2003


17

Gravitational Capture by SMBH• Recent strong progress on self-

interaction problem (restricted two-body problem) in GR. Accurate orbit calculations in near future.

• Complexity of waveform family poorly understood, work needed on hierarchical methods.

• Confusion with more distant sources possible, especially if population is large.

• Great interest in testing GR.

Population:

Waveform:


Data analysis:


24 April 2003


18

Gravitational Wave Pulsars• Effective ellipticity of NSs not

known, spindown bounds may be weak limits.

• Physics involves crust, core.• MS PSRs may reach spindown

bound (Cutler).• LIGO data analysis very

challenging, a prototype for LISA gravitational capture searches.

• Accurate positions (arcsecond) will lead to follow-up observations in radio, X-ray.

Population:

Waveform:


Data analysis:


24 April 2003


19

Neutron Star Vibrations• r-modes visible in Adv LIGO, may

limit spin of LMXBs. Viscosity wipes out r-modes in young stars.

• f-, p-modes of NSs excited during formation (hot stars) and probably during glitches, X-ray bursts from magnetars, etc. Need broad-band high-frequency detector to look for these.

• Payoff: NS asteroseismology, insight into EOS and other physics

Population:

Waveform:


Data analysis:


24 April 2003


20

Gravitational Collapse• Numerical simulations needed here as

for BH problems. GR hydro codes improving, 3D simulations coming along, bigger computers needed.

• Physics probably under control, but initial conditions (esp. rotation) and high-density EOS uncertain.

• Pathways to NS or BH, -bursts, hypernovae: want associated waveforms!

• Data analysis for LIGO must be robust, not too dependent on waveform templates, hence sub-optimal. We don’t know how best to do this yet!

Population:

Waveform:


Data analysis:


24 April 2003


21

Unexpected sources• LISA particularly has high sensitivity,

can see some sources w/o filtering, or with short FFTs w no demodulation.

• LIGO/GEO/VIRGO may see coincident events of unknown origin.

• Search methods in data: many possible methods, no clear performance criteria. Need to run several at once.

• 30% of the Universe is in matter that can emit no electromagnetic radiation. Is it really so smooth that all the interesting structure and dynamics is in the 4% that carries charge? Only GW observations can answer this!

Population:

Waveform:


Data analysis:

Documents

Sources of Gravitational Waves: an Overview Bernard Schutz Albert Einstein Institute Potsdam, Germany @aei.mpg.de